WASHINGTON  Working well past midnight, a weary Senate was mowing down a parade of Republican proposals aimed at undercutting President Barack Obama's signature health care law as Democrats push toward final passage of the companion piece to his overhaul plan.

In a voting marathon that began the previous afternoon, senators were voting early Thursday on an uninterrupted stream of GOP amendments to a measure altering the new health law. The president was flying to Iowa later in the day for the first of many appearances he will make around the country before the fall congressional elections to sell his health care revamp.

Obama was appearing in Iowa City, where as a presidential candidate in 2007 he touted his ideas for health coverage for all. His trip comes with polls showing people are divided over the law he signed Tuesday, and Democratic lawmakers from competitive districts hoping he can convince more voters by November that it was the right move.

Adding an ominous undertone to the political clashes, Obama's barnstorming comes as the FBI says it is investigating threats and vandalism against congressional Democrats who backed the health legislation.

At least 10 Democratic lawmakers had reported such incidents as of Wednesday. These include a brick tossed through a window of the Niagara Falls, N.Y., office of Rep. Louise Slaughter and threats received by the office of Michigan Rep. Bart Stupak, an anti-abortion leader who accepted White House assurances on limiting the procedure.

The Senate, meanwhile, set out to complete a bill making changes in the health law. It was being considered under rules allowing its passage by a simple majority instead of 60 votes in the 100-seat chamber, making its approval virtually inevitable.

But first, Democrats ran into a mountain of GOP amendments. Outnumbered and all but assured of defeat, Republicans nonetheless forced votes on amendments aimed at reshaping the measure - or at least forcing Democrats to take votes that could be used against them in TV ads in the fall campaigns.

"There's no attempt to improve the bill. There's an attempt to destroy this bill," said an exasperated Senate Majority Leader Harry Reid, D-Nev.

"The majority leader may not think we're serious about changing the bill, but we'd like to change the bill, and with a little help from our friends on the other side we could improve the bill significantly," answered Senate Minority Leader Mitch McConnell, R-Ky.

Senators had voted on 28 consecutive GOP amendments as 2:30 a.m. approached and were still working through a series of votes that began at 5:30 the previous afternoon. No clear end was in sight.

By 57-42, Democrats rejected an amendment by Sen. Tom Coburn, R-Okla., barring federal purchases of Viagra and other erectile dysfunction drugs for sex offenders. Coburn said it would save millions, while Sen. Max Baucus, D-Mont., called it "a crass political stunt."

Democrats also deflected GOP amendments rolling back the health law's Medicare cuts; killing extra Medicaid funds for Tennessee and other state-specific spending; barring tax increases for families earning under $250,000; and requiring the president and other administration officials to purchase health care from exchanges the statute creates.